Chat is not e-mail. It's chat. It has a much different feel to it. One brings a different mental context to e-mail than they do to chat. It is accessed differently, and the use patterns are very different. Hence, solving "offline chat" by sending an e-mail... this is not a real solution.

You could argue that some of the characteristics we find in chat are not useful, counter productive, etc. And there is probably some truth to that. But that is a different argument than what you made.